function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
%   theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by 
%   taking num_iters gradient steps with learning rate alpha

% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);

for iter = 1:num_iters

    % ====================== YOUR CODE HERE ======================
    % Instructions: Perform a single gradient step on the parameter vector
    %               theta. 
    %
    % Hint: While debugging, it can be useful to print out the values
    %       of the cost function (computeCost) and gradient here.
    %

    J_1 = 0;
    J_2 = 0;
    for i = 1:m
        J_1 = J_1 + ( theta( 1 ) * X( i, 1 ) + theta( 2 ) * X( i, 2 ) - y( i ) ) * X( i, 1 );
        J_2 = J_2 + ( theta( 1 ) * X( i, 1 ) + theta( 2 ) * X( i, 2 ) - y( i ) ) * X( i, 2 );
    end

    theta( 1 ) = theta( 1 ) - alpha * J_1 / m;
    theta( 2 ) = theta( 2 ) - alpha * J_2 / m;

    % ============================================================

    % Save the cost J in every iteration    
    J_history(iter) = computeCost(X, y, theta);

end

J_history

end
